Two-mode Gaussian product states in a lossy interferometer

The quantum Fisher information for a two-mode, Gaussian product state in an interferometer subject to photon loss is studied. We obtain the quantum Cramer–Rao bound on the achievable precision in phase estimation using such states. The scaling of the measurement precision with the mean photon number is compared to the shot noise-limited scaling for dual squeezed vacuum states and dual squeezed, displaced vacuum states.